CAIRO — On the eve of his first trip to the United States as Egypt’s new Islamist president, Mohamed Morsi said the United States needed to fundamentally change its approach to the Arab world, showing greater respect for its values and helping build a Palestinian state, if it hoped to overcome decades of pent-up anger.

A former leader of the Muslim Brotherhood and Egypt’s first democratically elected president, Mr. Morsi sought in a 90-minute interview with The New York Times to introduce himself to the American public and to revise the terms of relations between his country and the United States after the ouster of Hosni Mubarak, an autocratic but reliable ally.

He said it was up to Washington to repair relations with the Arab world and to revitalize the alliance with Egypt, long a cornerstone of regional stability.

If Washington is asking Egypt to honor its treaty with Israel, he said, Washington should also live up to its own Camp David commitment to Palestinian self-rule. He said the United States must respect the Arab world’s history and culture, even when that conflicts with Western values.

And he dismissed criticism from the White House that he did not move fast enough to condemn protesters who recently climbed over the United States Embassy wall and burned the American flag in anger over a video that mocked the Prophet Muhammad.

“We took our time” in responding to avoid an explosive backlash, he said, but then dealt “decisively” with the small, violent element among the demonstrators.

“We can never condone this kind of violence, but we need to deal with the situation wisely,” he said, noting that the embassy employees were never in danger.

Mr. Morsi, who will travel to New York on Sunday for a meeting of the United Nations General Assembly, arrives at a delicate moment. He faces political pressure at home to prove his independence, but demands from the West for reassurance that Egypt under Islamist rule will remain a stable partner.

Mr. Morsi, 61, whose office was still adorned with nautical paintings that Mr. Mubarak left behind, said the United States should not expect Egypt to live by its rules.

“If you want to judge the performance of the Egyptian people by the standards of German or Chinese or American culture, then there is no room for judgment,” he said. “When the Egyptians decide something, probably it is not appropriate for the U.S. When the Americans decide something, this, of course, is not appropriate for Egypt.”

He suggested that Egypt would not be hostile to the West, but would not be as compliant as Mr. Mubarak either.

“Successive American administrations essentially purchased with American taxpayer money the dislike, if not the hatred, of the peoples of the region,” he said, by backing dictatorial governments over popular opposition and supporting Israel over the Palestinians.

He initially sought to meet with President Obama at the White House during his visit this week, but he received a cool reception, aides to both presidents said. Mindful of the complicated election-year politics of a visit with Egypt’s Islamist leader, Mr. Morsi dropped his request.

His silence in the immediate aftermath of the embassy protest elicited a tense telephone call from Mr. Obama, who also told a television interviewer that at that moment he did not consider Egypt an ally, if not an enemy either. When asked if he considered the United States an ally, Mr. Morsi answered in English, “That depends on your definition of ally,” smiling at his deliberate echo of Mr. Obama. But he said he envisioned the two nations as “real friends.”

Mr. Morsi spoke in an ornate palace that Mr. Mubarak inaugurated three decades ago, a world away from the Nile Delta farm where the new president grew up, or the prison cells where he had been confined by Mr. Mubarak for his role in the Brotherhood. Three months after his swearing-in, the most noticeable change to the presidential office was a plaque on his desk bearing the Koranic admonition, “Be conscious of a day on which you will return to God.”

A stocky figure with a trim beard and wire-rim glasses, he earned a doctorate in materials science at the University of Southern California in the early 1980s. He spoke with an easy confidence in his new authority, reveling in an approval rating he said was at 70 percent. When he grew animated, he slipped from Arabic into crisp English.

Little known at home or abroad until just a few months ago, he was the Brotherhood’s second choice as a presidential nominee after the first choice was disqualified. On the night of the election, the generals who had ruled since Mr. Mubarak’s ouster issued a decree keeping most presidential powers for themselves.

But last month Mr. Morsi confounded all expectations by prying full executive authority back from the generals. In the interview, when an interpreter suggested that the generals had “decided” to exit politics, Mr. Morsi quickly corrected him.

“No, no, it is not that they ‘decided’ to do it,” he interjected in English, determined to clarify that it was he who removed them. “This is the will of the Egyptian people through the elected president, right?

“The president of the Arab Republic of Egypt is the commander of the armed forces, full stop. Egypt now is a real civil state. It is not theocratic, it is not military. It is democratic, free, constitutional, lawful and modern.”

He added, “We are behaving according to the Egyptian people’s choice and will, nothing else — is it clear?”

He praised Mr. Obama for moving “decisively and quickly” to support the Arab Spring revolutions, and he said he believed that Americans supported “the right of the people of the region to enjoy the same freedoms that Americans have.”

Arabs and Americans have “a shared objective, each to live free in their own land, according to their customs and values, in a fair and democratic fashion,” he said, adding that he hoped for “a harmonious, peaceful coexistence.”

But he also argued that Americans “have a special responsibility” for the Palestinians because the United States had signed the 1978 Camp David accord. The agreement called for the withdrawal of Israeli troops from the West Bank and Gaza and for full Palestinian self-rule.

“As long as peace and justice are not fulfilled for the Palestinians, then the treaty remains unfulfilled,” he said.

He made no apologies for his roots in the Brotherhood, the insular religious revival group that was Mr. Mubarak’s main opposition and now dominates Egyptian politics.

“I grew up with the Muslim Brotherhood,” he said. “I learned my principles in the Muslim Brotherhood. I learned how to love my country with the Muslim Brotherhood. I learned politics with the Brotherhood. I was a leader of the Muslim Brotherhood.”

He left the group when he took office but remains a member of its political party. But he said he sees “absolutely no conflict” between his loyalty to the Brotherhood and his vows to govern on behalf of all, including members of the Christian minority or those with more secular views.

“I prove my independence by taking the correct acts for my country,” he said. “If I see something good from the Muslim Brotherhood, I will take it. If I see something better in the Wafd” — Egypt’s oldest liberal party — “I will take it.”

He repeatedly vowed to uphold equal citizenship rights of all Egyptians, regardless of religion, sex or class. But he stood by the religious arguments he once made as a Brotherhood leader that neither a woman nor a Christian would be a suitable president.

“We are talking about values, beliefs, cultures, history, reality,” he said. He said the Islamic position on presidential eligibility was a matter for Muslim scholars to decide, not him. But regardless of his own views or the Brotherhood’s, he said, civil law was another matter.

“I will not prevent a woman from being nominated as a candidate for the presidential campaign,” he said. “This is not in the Constitution. This is not in the law. But if you want to ask me if I will vote for her or not, that is something else, that is different.”

He was also eager to reminisce about his taste of American culture as a graduate student at the University of Southern California. “Go, Trojans!” he said, and he remembered learning about the world from Barbara Walters in the morning and Walter Cronkite at night. “And that’s the way it is!” Mr. Morsi said with a smile.

But he also displayed some ambivalence. He effused about his admiration for American work habits, punctuality and time management. But when an interpreter said that Mr. Morsi had “learned a lot” in the United States, he quickly interjected a qualifier in English: “Scientifically!”

He was troubled by the gangs and street of violence of Los Angeles, he said, and dismayed by the West’s looser sexual mores, mentioning couples living together out of wedlock and what he called “naked restaurants,” like Hooters.

“I don’t admire that,” he said. “But that is the society. They are living their way.”